Question:
Find a formula for the volume of this trapezoid (rotates 360 degrees around the x-axis):
R= big radius
r= small radius
h= height

The area is equal to:

Volume of an object rotating around the x-axis:

Judging by the graph, it starts from x=0, and it ends on x=h, therefore the interval is [0;h].

The area function is the equation for a trapezoid, therefore, the function.

Conclusion:

Did I solve this correctly? I'm afraid, the "dh" is wrong, and generally just unsure if I solved this correctly.

Hi

You did not solve correctly !
This formula is applied to solid whose frontier is generated by the rotation of a curve whose equation is y=f(x) around x axis
The function to be taken into account is therefore the line joining the point (0,R) to the point (h,r)
You have to integrate